Problem: Simplify the following expression: $\sqrt{2}+\sqrt{18}+\sqrt{8}$
Answer: First, try to factor any perfect squares out of the radicals. $= \sqrt{2}+\sqrt{18}+\sqrt{8}$ $= \sqrt{2}+\sqrt{9 \cdot 2}+\sqrt{4 \cdot 2}$ Separate the radicals and simplify. $= \sqrt{2}+\sqrt{9} \cdot \sqrt{2}+\sqrt{4} \cdot \sqrt{2}$ $= \sqrt{2}+3\sqrt{2}+2\sqrt{2}$ Finally, simplify by combining the terms. $= ( 1 + 3 + 2 )\sqrt{2} = 6\sqrt{2}$